\section{Samples} 
\label{sec:samples}

The samples used in this analysis come from AMPT 1.26t1b. The frame is Au-Au collision. The impact parameter is 8 fm. The parton screening mass is 3.2264 $fm^{-1}$. $\alpha$ sets in parton cascade is 0.33. 
600,000 events are used in this analysis. The first step is to convert the output files from AMPT to root files. Two files are used for parton level study. The first file is "parton-initial-afterPropagation.dat"
which outputs the complete information of partons that enter the parton cascade; i.e., it gives the minijet gluon information for default runs, or the quark and anti-quark information after string melting (before parton cascade) for string melting runs.
This output is stored in root file as the initial parton informaion. And then we use "parton-collisionsHistory.dat" which is collisions history. 
Each collision recorded in the history file has 4 lines. The first 2 lines are incoming partons information and last 2 lines are outcoming partons information. 
We have to compare the outcoming partons with the incoming partons of other collisions which happend after (we can judge it from time information).
Based on the parton momentum , position and PDGId, we trace the parton from initial status to make a "collision chain" to final parton, which parton will not collide anymore. 
After getting the chain of a parton collision, we can know the number of collision of each parton. And all the information before the parton collide on other partons ( we call it initial parton) and this parton after all collision( final parton). 
Then we can research on the change of momentum or position of partons before and after the collisions.

First target is the distribution of number of collisions. In order to distinguish high $P_T$ and low $P_{T}$ samples' performence, we take two certain phase spaces which are $P_{T}<0.5GeV$ and $P_{T}>3GeV$. 
To study more details about momentum space, we draw the initial $P_{T}$ and final $P_{T}$ 2D histogram. 
And the relationship between number of collisions and $\Delta P_{T}$, which is difference of $P_{T}$ of initial and final partons.
Then we turn to azimuth angle. We want to study the relationship between azimuth angle, momentum and number of collisions. Generally we use v2 to show the information of azimuth angle. We get v2 from fitting the $cos(\phi )$ using function $p_{0}*[1+2p_{1}cos*(2\phi )]$, where $p_{1}$ is v2.
In this analysis, we reserch on both v2 as a function of $P_{T}$ and v2 as a function of number of collision.
In v2 vs number of collisions study, we choose initial $P_{T}<0.5GeV$, $1GeV<P_{T}<2GeV$ and $P_{T}>3GeV$ regions to show v2 performe50e of different parton.
In v2 vs $P_{T}$ study, we choose 4 situations, which are number of collisions is 0,1,2 and more than 2, so that will reveal more information.
